山东建筑大学计算机学院算法分析算法复习题(Yuconan翻译)

1.The O-notation provides an asymptotic upper bound. The Ω-notation provides an

asymptotic lower bound. The Θ-notation asymptotically a function form above

2.To represent a heap as an array，the root of tree is A[1], and given the index i of a

node, the indices of its parent Parent(i) { return ⎣i/2⎦; }，left child, Left(i)

{ return 2*i; }，right child, right(i) { return 2*i + 1; }.

代表一个堆中的一个数组，树的根节点是A[1]，并且给出一个节点i，那么该节点的父节点是左孩子右孩子

3.Because the heap of n elements is a binary tree, the height of any node is at most

Θ(lg n).

因为n个元素的堆是一个二叉树，任意节点的树高最多是

4.In optimization problems, there can be many possible solutions. Each solution

has a value, and we wish to find a solution with the optimal (minimum or maximum) value. We call such a solution an optimal solution to the problem.

在最优化问题中，有很多可能的解，每个解都有一个值，我们希望找到一个最优解（最大或最小），我们称这个解为最优解问题。

5.optimal substructure if an optimal solution to the problem contains within it

optimal solutions to subproblems.

最优子结构中问题的最优解，至少包含它的最优解的子问题。

6. A subsequence of X if there exists a strictly increasing sequence of

indices of X such that for all j = 1, 2, ..., k, we have x i j= z j .

Let X = and Y = be sequences, and let Z =

z2, ..., z k> be any LCS of X and Y.

(1). If x m = y n, then z k = x m = y n and Z k-1 is an LCS of X m-1 and Y n-1.

(2). If x m ≠ y n, then z k ≠ x m implies that Z is an LCS of X m-1 and Y.

(3). If x m ≠ y n, then z k ≠ y n implies that Z is an LCS of X and Y n-1.

7. A greedy algorithm always makes the choice that looks best at the moment. That

is, it makes a locally optimal choice in the hope that this choice will lead to a

globally optimal solution.

贪心算法经常需要在某个时刻寻找最好的选择。正因如此，它在当下找到希望中的最优选择，以便引导出一个全局的最优解。

8.The greedy-choice property and optimal sub-structure are the two key ingredients

of greedy algorithm.

贪心选择和最优子结构是贪心算法的两个重要组成部分。

9.When a recursive algorithm revisits the same problem over and over again, we

say that the optimization problem has overlapping subproblems.

当一个递归算法一遍一遍的遍历同一个问题时，我们说这个最优化问题是重叠子问题。

10.greedy-choice property is a globally optimal solution can be arrived at by making

a locally optimal (greedy) choice.

贪心选择性质是一个全局的最优解，这个最优解可以做一个全局的最优选择。

11.An approach of Matrix multiplication can develope a Θ(V4)-time algorithm for

the all-pairs shortest-paths problem and then improve its running time to Θ(V3lg V).

一个矩阵相乘问题的解决可以一个时间复杂度算法的所有路径的最短路径问题，改进后的时间复杂度是。

12.Floyd-Warshall algorithm, runs in Θ(V3) time to solve the all-pairs

shortest-paths problem.

FW算法在时间复杂度下可以解决最短路径问题。

13.The running time of Quick Sort is O(n2) in the worst case, and O(n lg n) in the

average case.

快速排序的平均时间复杂度是O(n lg n)，最坏时间复杂度是O(n2)。

14.The MERGE(A,p,q,r) procedure in merge sort takes time Θ(n).

MERGE在归并排序中所花费的时间是。

15.Given a weighted, directed graph G = (V, E) with source s and weight function w :

E →R, the Bellman-Ford algorithm makes |V| - 1 passes over the edges of the

graph.

给一个带权重的有向图G = (V, E)，权重关系w : E →R,则the Bellman-Ford算法需经过条边。

16.The Bellman-Ford algorithm runs in time O(V E).

Bellman ford 算法的时间复杂度是。

17.A decision tree represents the comparisons made by a comparison sort.The

asymptotic height of any decision tree for sorting n elements is Ω(n lg n).

一个决策树代表一个比较类型，通过比较排序。N个元素的任意决策树的渐进高度是。True-false questions

1.An algorithm is said to be correct if, for some input instance, it halts with the

correct output F

如果给一个算法输入一些实例，并且它给力正确的输出，则认识这个算法是正确的。

2.Insertion sort always best merge sort F

插入排序总是优越与归并排序。

3.Θ(n lg n) grows more slowly than Θ(n2). Therefore, merge sort asymptotically

beats insertion sort in the worst case. T

Θ(n lg n)

4.Currently computers are fast and computer memory is very cheap, we have no

reason to study algorithms. F

5.In RAM (Random-Access Machine) model, instructions are executed with

concurrent operations. F

6.The running time of an algorithm on a particular input is the number of primitive

operations or “steps” executed. T

7.Quick sorts, have no combining step: two subarrays form an already-sorted array.

T

8.The running time of Counting sort is O(n + k). But the running time of sorting is

Ω(n lg n). So this is contradiction. F

9.The Counting sort is stable. T

10.In the selection problem,there is a algorithm of theoretical interest only with O(n)

worst-case running time. T

11.Divide-and-conquer algorithms partition the problem into independent

subproblems, solve the subproblems recursively, and then combine their solutions